Inertial viscosity forward–backward splitting algorithm for monotone inclusions and its application to image restoration problems

ABSTRACT

In this research, we are interested about the monotone inclusion problems in the scope of the real Hilbert spaces by using an inertial forward–backward splitting algorithm. In addition, we have discussed the application of this algorithm.

KEYWORDS:

• Inertial algorithm
• inertial splitting algorithm
• forward–backward algorithm
• monotone inclusion problems

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 46T99
• 47H20
• 49M20
• 49M25
• 49M27

Acknowledgments

This work was completed while the first author visit Prof. Juan Martínez-Moreno at Faculty of Science, Department of Mathematics University of Jaén, Spain.. The authors thank very much Prof. Juan Martínez-Moreno for his hospitality and support

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Duangkamon Kitkuan http://orcid.org/0000-0002-9854-9864

Poom Kumam http://orcid.org/0000-0002-5463-4581

Juan Martínez-Moreno http://orcid.org/0000-0002-3340-2781

Kanokwan Sitthithakerngkiet http://orcid.org/0000-0002-8496-7803

Additional information

Funding

The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Moreover, Kanokwan Sitthithakerngkiet was funded by King Mongkut's University of Technology North Bangkok, Contract No. KMUTNB-62-KNOW-40. Furthermore, Duangkamon Kitkuan was supported by the “Petchra Pra Jom Klao Ph.D. Research Scholarship from King Mongkut's University of Technology Thonburi” (Grant No.10/2559). Thailand Research Fund (TRF) and the King Mongkut's University of Technology Thonburi (KMUTT) under the TRF Research Scholar Award RSA6080047.